Time · Clocks and Frequency

01From oscillation to reading · Clock Model

ASD explains clock-frequency changes through the interaction of the timing structure with its spatial state. In gravity, the background first changes the characteristic scale and associated wavelength of a standard process; at the same local vacuum propagation speed and common reference calibration, frequency and period change, and accumulated oscillations determine the display. We proceed from the phase length of one cycle to the static scale–frequency relation, then connect that analytic relation to clock technologies and comparison links.

Chapter 2 discusses periods through propagation or phase processes. For an atomic standard, $S_{\mathrm{cyc}}$ is a characteristic phase length defined by the period. It is neither an electron trajectory nor a photon round trip inside the atom. Defining an equivalent length and determining its environmental response are separate steps.

02Technologies and physical inputs · Clock Technologies

This table organizes the apparatus tasks implied by the manuscript; it does not claim six completed microscopic ASD clock models. BIPM realization guidance describes the local second as a unit of proper time and addresses realization and comparison corrections. Its metrological procedures are cited here without recasting them as ASD ontology. BIPM: practical realization of the second

03Scale coupling in gravity · Scale and Frequency

Equation (2.2a) of the final manuscript is an exact ratio, not merely the weak-field expression. With $\Phi=\Omega^{-1}=\sqrt{1+2\Psi/c^2}$, the specified static background and common reference calibration give:

Here $\Phi$ is a dimensionless line-density coefficient, not a volume density; $\Psi$ has dimensions of speed squared, and both positions require $1+2\Psi/c^2>0$. The isolated spherical exterior solution uses $\Psi=-G_0M/r$. This constitutive model supplies the full analytic ratio. Expanding to first order when $|\Psi|/c^2\ll1$ at both positions gives:

Chapter 2’s potential convention has $\Psi<0$ near a positive mass. At weak-field order, moving to higher potential gives a higher relative frequency in the first-order expansion of Eq. (2.2a). Weak-field redshift constrains a low-order relation; it does not uniquely determine a full strong-field scale law. The current gravitational-redshift topic develops the background, scale law and scope. This page explains the interface between standard processes and frequency readings; the full static background still requires that topic’s stated constitutive relation and does not follow from weak-field frequency shifts alone.

Here $f(r)$ is the frequency of the same class of standard process expressed against a common reference. The cycle-count discussion distinguishes it from nominal clock readings and the frequency after transmission to a receiver. A transfer link or directional-clock output still requires its own apparatus model.

04Published observations and interpretation · Experimental Relations

05A direction for discriminatory work · Proposed Comparison

06Review conditions and sources · Review and Sources

1. Definition and coupling: $S_{\mathrm{cyc}}=c/f$ defines a phase length. Predicting $f$ requires an independently specified background response of $S_{\mathrm{cyc}}$.
2. Local and remote quantities: Specify the references for $f_0,f(r)$, length scales and transfer signals in Eq. (2.2). Commonly calibrated quantities are not automatically raw local display values.
3. Clock technologies: Atomic transitions, cavity boundaries and mechanical structures require individual response models. Their universality must follow from those models.
4. Moving-clock continuity: How Chapter 1 Eq. (1.47)’s directional path expression enters an accumulated clock difference still requires examination. This page preserves LVE v1.1’s status and question.

These are conditions and matching tasks, without changing Chapter 2’s spatial-scale interpretation. Response coefficients, fits and precision targets absent from the manuscript are not supplied here.